The discussion centers on the challenges of applying Hamiltonian mechanics to Young's Double Slit Experiment due to the constraints on particle movement through the slits. There is a question about the feasibility of using constrained Hamiltonians in this context, suggesting that H could equal zero under certain conditions. Participants also explore the applicability of Feynman paths when the paths are restricted to a specific surface, such as a four-sphere. The complexities of these theoretical frameworks raise important questions about particle behavior in constrained environments. Overall, the conversation highlights the intricate relationship between quantum mechanics and mathematical formulations in physics.